The function F(x)= 1- e-x-xe-x for 0 < x < ∞ and 0 for x< 0 is the CDF of a random variable X. Using R: a) Using R, create a user-defined function for F(named F) in the interval [0,0). b) Using this F, find the probability that X ≤ 6 c) Using F, find the probability that X > 6 d) Using F, find the probability that 2 < X < 4

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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The function F(x)= 1 - e¯x- x·e¯x for 0 < x < ∞ and 0 for x< 0 is the CDF of a random variable X.
Using R:
a) Using R, create a user-defined function for F(named F) in the interval [0,00).
b) Using this F, find the probability that X ≤ 6
c) Using F, find the probability that X > 6
d) Using F, find the probability that 2 < X < 4
e) What is the probability density function(in R code) for x ≥ 0 ?
f) Paste your R script in the following box
16
Transcribed Image Text:The function F(x)= 1 - e¯x- x·e¯x for 0 < x < ∞ and 0 for x< 0 is the CDF of a random variable X. Using R: a) Using R, create a user-defined function for F(named F) in the interval [0,00). b) Using this F, find the probability that X ≤ 6 c) Using F, find the probability that X > 6 d) Using F, find the probability that 2 < X < 4 e) What is the probability density function(in R code) for x ≥ 0 ? f) Paste your R script in the following box 16
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